This paper is concerned with the numerical solution of the mixed Volterra-Fredholm integral equations by using a version of the block by block method. This method efficient for linear and nonlinear equations and it avoids the need for spacial starting values. The convergence is proved and finally performance of the method is illustrated by means of some significative examples.

Potassium dihydrogen phosphate, KH2PO4 (KDP) crystal is an excellent electro-optical nonlinear optical crystal with large electro-optical nonlinear coefficient, high laser damage threshold, and laser frequency doubling effect, electro-optical effect , Piezoelectric effects and other special features, widely used in inertial confinement fusion engineering (ICF) and electro-optical switching devices. Therefore, its growth mechanism, growth process and performance have been systematically studied. In the process of KDP crystal growth, it is found that the stability of the growth solution is an important factor affecting the quality of crystal growth. Therefore, in recent years, more and more research on the stability of the solution, such as the study of ph, doping, supersaturation, overheating time on the stability of the solution. Among them, the research on the doping is mostly reported, and the research on this aspect is mainly focused on two aspects. On the one hand, it is the study of the stability of the solution under doping, and the other is the effect of doping on the optical quality of the crystal. In fact, the stability of the growth solution and the quality of crystal growth is directly related to the quality, but the existing research to isolate the two researches. Therefore, the experiment will be carried out in the case of double-doped KDP solution stability, KDP crystal growth and crystal optical quality and other experiments, and in-depth analysis of the impact of solution stability and crystal optical quality of the reasons, while the solution stability and The relationship between the optical quality of the crystal is briefly analyzed.

This study offers a focused examination on Xinfang system, China’s unique mechanism particularly on its ability and efficacy in mediating land disputes between farmers and governmental bodies for social governance purposes. Based on interviews with 10 farmers, the study elucidates the system has low entry barriers and user-friendly, thus fast becoming the preferred system option when dealing with land conflicts. Xinfang facilitates direct communication between farmers and government officials, thereby in line with the sociocultural conventions of the rural populace. The study also highlights several constraints. While the Xinfang system employs a multifaceted approach to conflict resolution, including negotiation and grassroots governmental intervention, it lacks legislative power and institutional authority that are required for effective management of more complex or multi-stakeholder land disputes. The study advocates for a comprehensive reassessment and subsequent reform of the Xinfang system, focusing particularly on its mechanisms and procedures for dispute resolution. Such reforms are not merely instrumental for the more robust safeguarding of farmers’ land rights, but also for enhancing the overall integrity and public trust in China’s legal and administrative frameworks.

The urgency of adapting urban areas to the increasing impacts of climate change has prompted the scientific community to seek new approaches in partnership with public entities and civil society organizations. In Malaysia, Penang Island has developed a nature-based urban climate adaptation program (PNBCAP) seeking to increase urban resilience, reduce urban heat and flooding, strengthening social resilience, and build institutional capacity. The project includes a strong knowledge transfer component focused on encouraging other cities in the country to develop and implement adaptation policies, projects, and initiatives. This research develops a model adopting the most efficient processes to accelerate the transfer of knowledge to promote urban adaptation based on the PNBCAP. The methodology is developed based on a review of literature focused on innovation systems and change theories. The integration of success strategies in adaptation contributes to informing the creation of solutions around the alliance of local, state, and national government agencies, scientific institutions, and civil society organizations, in a new framework designated the Malaysian Adaptation Sharing Hub (MASH). MASH is structured in 3-steps and will function as an accelerator for the implementation of urban climate adaptation policies, with the target of creating 2 new adaptation-related policies to be adopted annually by each city member, based on knowledge gathered in the PNBCAP. It is concluded that, to speed up urban adaptation, it is necessary to reinforce and promote the sharing of knowledge resulting from or associated with pilot projects.

With the rapid development of global e-commerce, cross-border e-commerce has become an important force in promoting international trade and economic globalization. Due to the rapid development of cross-border e-commerce, the number of online disputes is gradually increasing. These disputes demonstrate their complexity and diversity in terms of legal application, evidence acquisition, and enforcement. Tmall Global is a cross-border e-commerce platform under the Chinese e-commerce giant Alibaba Group. This study takes Tmall Global as an example to analyze the characteristics of disputes on this platform and explore the current situation of online disputes in cross-border e-commerce. Drawing on the experience of online dispute resolution in the European Union, ASEAN, and other regions, this article proposes a series of suggestions to improve China’s cross-border e-commerce online dispute resolution mechanism, including enhancing the platform’s own dispute resolution capabilities, strengthening international cooperation and artificial intelligence, optimizing dispute resolution processes using large data and cloud computing, strengthening consumer rights protection, and optimizing legal and regulatory frameworks. The aim is to provide an effective dispute resolution mechanism for China’s cross-border e-commerce platforms and provide useful reference for other countries.

The electro-magnetic (EM) waves transmitted through a thin object with fine structures are observed by a microsphere located above the thin object. The EM radiation transmitted through the object produces both evanescent waves, which include information on the fine structures of the object (smaller than a wavelength), and propagating waves, which include the large image of the object (with dimensions larger than a wavelength). The super-resolutions are calculated by using the Helmholtz equation. According to this equation, evanescent waves have an imaginary component of the wavevector in the z direction, leading the components of the wavevector in the transversal directions to become very large so that the fine structures of the object can be observed. Due to the decay of the evanescent waves, only a small region near the contact point between the thin object and the microsphere is effective for producing the super resolution effects. The image with super-resolution can be increased by a movement of the microsphere over the object or by using arrays of microspheres. Both propagating and evanescent waves arrive at the inner surface of the microsphere. A coupling between the transmitted EM waves and resonances produced in the dielectric sphere, possibly obtained by the Mie method, leads to a product of the EM distribution function with the transfer function. While this transfer function might be calculated by the Mie method, it is also possible to use it as an experimental function. By Fourier transform of the above product, we get convolution between the EM spatial modes and those of the transfer function arriving at the nano-jet, which leads the evanescent waves to become propagating waves with effective very small wavelengths and thus increase the resolution.